LMFDB - Embedded newform 6002.2.a.b.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6002,2,Mod(1,6002)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6002, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6002 = 2 \cdot 3001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6002.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$47.9262112932$
Analytic rank:	$1$
Dimension:	$56$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6002.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.97926 q^{3} +1.00000 q^{4} -2.47117 q^{5} +2.97926 q^{6} +1.46435 q^{7} -1.00000 q^{8} +5.87597 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.97926 q^{3} +1.00000 q^{4} -2.47117 q^{5} +2.97926 q^{6} +1.46435 q^{7} -1.00000 q^{8} +5.87597 q^{9} +2.47117 q^{10} +6.41318 q^{11} -2.97926 q^{12} +0.478590 q^{13} -1.46435 q^{14} +7.36226 q^{15} +1.00000 q^{16} -2.53209 q^{17} -5.87597 q^{18} +5.17652 q^{19} -2.47117 q^{20} -4.36269 q^{21} -6.41318 q^{22} +0.382547 q^{23} +2.97926 q^{24} +1.10670 q^{25} -0.478590 q^{26} -8.56826 q^{27} +1.46435 q^{28} -2.45914 q^{29} -7.36226 q^{30} -7.92354 q^{31} -1.00000 q^{32} -19.1065 q^{33} +2.53209 q^{34} -3.61867 q^{35} +5.87597 q^{36} -9.71833 q^{37} -5.17652 q^{38} -1.42584 q^{39} +2.47117 q^{40} +7.86215 q^{41} +4.36269 q^{42} -1.14193 q^{43} +6.41318 q^{44} -14.5205 q^{45} -0.382547 q^{46} +4.03015 q^{47} -2.97926 q^{48} -4.85567 q^{49} -1.10670 q^{50} +7.54375 q^{51} +0.478590 q^{52} -7.92448 q^{53} +8.56826 q^{54} -15.8481 q^{55} -1.46435 q^{56} -15.4222 q^{57} +2.45914 q^{58} +12.9777 q^{59} +7.36226 q^{60} +0.0523156 q^{61} +7.92354 q^{62} +8.60450 q^{63} +1.00000 q^{64} -1.18268 q^{65} +19.1065 q^{66} -12.0780 q^{67} -2.53209 q^{68} -1.13971 q^{69} +3.61867 q^{70} -11.7843 q^{71} -5.87597 q^{72} +8.80716 q^{73} +9.71833 q^{74} -3.29715 q^{75} +5.17652 q^{76} +9.39116 q^{77} +1.42584 q^{78} +15.4565 q^{79} -2.47117 q^{80} +7.89912 q^{81} -7.86215 q^{82} +7.15355 q^{83} -4.36269 q^{84} +6.25724 q^{85} +1.14193 q^{86} +7.32642 q^{87} -6.41318 q^{88} -18.0098 q^{89} +14.5205 q^{90} +0.700826 q^{91} +0.382547 q^{92} +23.6063 q^{93} -4.03015 q^{94} -12.7921 q^{95} +2.97926 q^{96} +8.49856 q^{97} +4.85567 q^{98} +37.6836 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9}+O(q^{10}) $ 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9	\( 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9} + 12 q^{11} - 11 q^{12} - 31 q^{13} + 21 q^{14} - 22 q^{15} + 56 q^{16} - 4 q^{17} - 53 q^{18} - 9 q^{19} + 13 q^{21} - 12 q^{22} - 39 q^{23} + 11 q^{24} + 8 q^{25} + 31 q^{26} - 44 q^{27} - 21 q^{28} + 13 q^{29} + 22 q^{30} - 35 q^{31} - 56 q^{32} - 26 q^{33} + 4 q^{34} - 7 q^{35} + 53 q^{36} - 65 q^{37} + 9 q^{38} - 27 q^{39} + 38 q^{41} - 13 q^{42} - 76 q^{43} + 12 q^{44} - 21 q^{45} + 39 q^{46} - 43 q^{47} - 11 q^{48} + 9 q^{49} - 8 q^{50} - 19 q^{51} - 31 q^{52} - 26 q^{53} + 44 q^{54} - 67 q^{55} + 21 q^{56} - 26 q^{57} - 13 q^{58} + 11 q^{59} - 22 q^{60} - 17 q^{61} + 35 q^{62} - 67 q^{63} + 56 q^{64} + 31 q^{65} + 26 q^{66} - 93 q^{67} - 4 q^{68} - 13 q^{69} + 7 q^{70} - 33 q^{71} - 53 q^{72} - 41 q^{73} + 65 q^{74} - 21 q^{75} - 9 q^{76} + 5 q^{77} + 27 q^{78} - 69 q^{79} + 36 q^{81} - 38 q^{82} + 4 q^{83} + 13 q^{84} - 40 q^{85} + 76 q^{86} - 69 q^{87} - 12 q^{88} + 40 q^{89} + 21 q^{90} - 64 q^{91} - 39 q^{92} - 57 q^{93} + 43 q^{94} - 22 q^{95} + 11 q^{96} - 71 q^{97} - 9 q^{98} + 17 q^{99}+O(q^{100}) \) 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9 + 12 * q^11 - 11 * q^12 - 31 * q^13 + 21 * q^14 - 22 * q^15 + 56 * q^16 - 4 * q^17 - 53 * q^18 - 9 * q^19 + 13 * q^21 - 12 * q^22 - 39 * q^23 + 11 * q^24 + 8 * q^25 + 31 * q^26 - 44 * q^27 - 21 * q^28 + 13 * q^29 + 22 * q^30 - 35 * q^31 - 56 * q^32 - 26 * q^33 + 4 * q^34 - 7 * q^35 + 53 * q^36 - 65 * q^37 + 9 * q^38 - 27 * q^39 + 38 * q^41 - 13 * q^42 - 76 * q^43 + 12 * q^44 - 21 * q^45 + 39 * q^46 - 43 * q^47 - 11 * q^48 + 9 * q^49 - 8 * q^50 - 19 * q^51 - 31 * q^52 - 26 * q^53 + 44 * q^54 - 67 * q^55 + 21 * q^56 - 26 * q^57 - 13 * q^58 + 11 * q^59 - 22 * q^60 - 17 * q^61 + 35 * q^62 - 67 * q^63 + 56 * q^64 + 31 * q^65 + 26 * q^66 - 93 * q^67 - 4 * q^68 - 13 * q^69 + 7 * q^70 - 33 * q^71 - 53 * q^72 - 41 * q^73 + 65 * q^74 - 21 * q^75 - 9 * q^76 + 5 * q^77 + 27 * q^78 - 69 * q^79 + 36 * q^81 - 38 * q^82 + 4 * q^83 + 13 * q^84 - 40 * q^85 + 76 * q^86 - 69 * q^87 - 12 * q^88 + 40 * q^89 + 21 * q^90 - 64 * q^91 - 39 * q^92 - 57 * q^93 + 43 * q^94 - 22 * q^95 + 11 * q^96 - 71 * q^97 - 9 * q^98 + 17 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.97926	−1.72007	−0.860037	−	0.510231i	$-0.829560\pi$
$3$	−2.97926	−1.72007	−0.860037	+	0.510231i	$0.829560\pi$
$4$	1.00000	0.500000
$5$	−2.47117	−1.10514	−0.552571	−	0.833466i	$-0.686353\pi$
$5$	−2.47117	−1.10514	−0.552571	+	0.833466i	$0.686353\pi$
$6$	2.97926	1.21628
$7$	1.46435	0.553474	0.276737	−	0.960946i	$-0.410747\pi$
$7$	1.46435	0.553474	0.276737	+	0.960946i	$0.410747\pi$
$8$	−1.00000	−0.353553
$9$	5.87597	1.95866
$10$	2.47117	0.781454
$11$	6.41318	1.93365	0.966823	−	0.255448i	$-0.0822229\pi$
$11$	6.41318	1.93365	0.966823	+	0.255448i	$0.0822229\pi$
$12$	−2.97926	−0.860037
$13$	0.478590	0.132737	0.0663685	−	0.997795i	$-0.478859\pi$
$13$	0.478590	0.132737	0.0663685	+	0.997795i	$0.478859\pi$
$14$	−1.46435	−0.391365
$15$	7.36226	1.90093
$16$	1.00000	0.250000
$17$	−2.53209	−0.614122	−0.307061	−	0.951690i	$-0.599346\pi$
$17$	−2.53209	−0.614122	−0.307061	+	0.951690i	$0.599346\pi$
$18$	−5.87597	−1.38498
$19$	5.17652	1.18757	0.593787	−	0.804622i	$-0.297632\pi$
$19$	5.17652	1.18757	0.593787	+	0.804622i	$0.297632\pi$
$20$	−2.47117	−0.552571
$21$	−4.36269	−0.952016
$22$	−6.41318	−1.36729
$23$	0.382547	0.0797665	0.0398833	−	0.999204i	$-0.487301\pi$
$23$	0.382547	0.0797665	0.0398833	+	0.999204i	$0.487301\pi$
$24$	2.97926	0.608138
$25$	1.10670	0.221341
$26$	−0.478590	−0.0938593
$27$	−8.56826	−1.64896
$28$	1.46435	0.276737
$29$	−2.45914	−0.456651	−0.228326	−	0.973585i	$-0.573325\pi$
$29$	−2.45914	−0.456651	−0.228326	+	0.973585i	$0.573325\pi$
$30$	−7.36226	−1.34416
$31$	−7.92354	−1.42311	−0.711555	−	0.702630i	$-0.752009\pi$
$31$	−7.92354	−1.42311	−0.711555	+	0.702630i	$0.752009\pi$
$32$	−1.00000	−0.176777
$33$	−19.1065	−3.32601
$34$	2.53209	0.434250
$35$	−3.61867	−0.611668
$36$	5.87597	0.979328
$37$	−9.71833	−1.59768	−0.798842	−	0.601541i	$-0.794554\pi$
$37$	−9.71833	−1.59768	−0.798842	+	0.601541i	$0.794554\pi$
$38$	−5.17652	−0.839742
$39$	−1.42584	−0.228318
$40$	2.47117	0.390727
$41$	7.86215	1.22786	0.613931	−	0.789360i	$-0.289587\pi$
$41$	7.86215	1.22786	0.613931	+	0.789360i	$0.289587\pi$
$42$	4.36269	0.673177
$43$	−1.14193	−0.174143	−0.0870715	−	0.996202i	$-0.527751\pi$
$43$	−1.14193	−0.174143	−0.0870715	+	0.996202i	$0.527751\pi$
$44$	6.41318	0.966823
$45$	−14.5205	−2.16460
$46$	−0.382547	−0.0564034
$47$	4.03015	0.587858	0.293929	−	0.955827i	$-0.405037\pi$
$47$	4.03015	0.587858	0.293929	+	0.955827i	$0.405037\pi$
$48$	−2.97926	−0.430019
$49$	−4.85567	−0.693667
$50$	−1.10670	−0.156511
$51$	7.54375	1.05634
$52$	0.478590	0.0663685
$53$	−7.92448	−1.08851	−0.544256	−	0.838919i	$-0.683188\pi$
$53$	−7.92448	−1.08851	−0.544256	+	0.838919i	$0.683188\pi$
$54$	8.56826	1.16599
$55$	−15.8481	−2.13695
$56$	−1.46435	−0.195683
$57$	−15.4222	−2.04272
$58$	2.45914	0.322901
$59$	12.9777	1.68955	0.844775	−	0.535122i	$-0.179734\pi$
$59$	12.9777	1.68955	0.844775	+	0.535122i	$0.179734\pi$
$60$	7.36226	0.950464
$61$	0.0523156	0.00669833	0.00334917	−	0.999994i	$-0.498934\pi$
$61$	0.0523156	0.00669833	0.00334917	+	0.999994i	$0.498934\pi$
$62$	7.92354	1.00629
$63$	8.60450	1.08407
$64$	1.00000	0.125000
$65$	−1.18268	−0.146693
$66$	19.1065	2.35185
$67$	−12.0780	−1.47556	−0.737779	−	0.675043i	$-0.764125\pi$
$67$	−12.0780	−1.47556	−0.737779	+	0.675043i	$0.764125\pi$
$68$	−2.53209	−0.307061
$69$	−1.13971	−0.137204
$70$	3.61867	0.432514
$71$	−11.7843	−1.39854	−0.699270	−	0.714858i	$-0.746492\pi$
$71$	−11.7843	−1.39854	−0.699270	+	0.714858i	$0.746492\pi$
$72$	−5.87597	−0.692490
$73$	8.80716	1.03080	0.515400	−	0.856950i	$-0.327643\pi$
$73$	8.80716	1.03080	0.515400	+	0.856950i	$0.327643\pi$
$74$	9.71833	1.12973
$75$	−3.29715	−0.380722
$76$	5.17652	0.593787
$77$	9.39116	1.07022
$78$	1.42584	0.161445
$79$	15.4565	1.73899	0.869496	−	0.493939i	$-0.164444\pi$
$79$	15.4565	1.73899	0.869496	+	0.493939i	$0.164444\pi$
$80$	−2.47117	−0.276286
$81$	7.89912	0.877680
$82$	−7.86215	−0.868229
$83$	7.15355	0.785204	0.392602	−	0.919709i	$-0.371575\pi$
$83$	7.15355	0.785204	0.392602	+	0.919709i	$0.371575\pi$
$84$	−4.36269	−0.476008
$85$	6.25724	0.678693
$86$	1.14193	0.123138
$87$	7.32642	0.785474
$88$	−6.41318	−0.683647
$89$	−18.0098	−1.90903	−0.954517	−	0.298158i	$-0.903628\pi$
$89$	−18.0098	−1.90903	−0.954517	+	0.298158i	$0.903628\pi$
$90$	14.5205	1.53060
$91$	0.700826	0.0734665
$92$	0.382547	0.0398833
$93$	23.6063	2.44786
$94$	−4.03015	−0.415678
$95$	−12.7921	−1.31244
$96$	2.97926	0.304069
$97$	8.49856	0.862898	0.431449	−	0.902137i	$-0.358002\pi$
$97$	8.49856	0.862898	0.431449	+	0.902137i	$0.358002\pi$
$98$	4.85567	0.490496
$99$	37.6836	3.78735
$100$	1.10670	0.110670
$101$	1.37483	0.136801	0.0684003	−	0.997658i	$-0.478210\pi$
$101$	1.37483	0.136801	0.0684003	+	0.997658i	$0.478210\pi$
$102$	−7.54375	−0.746942
$103$	−0.635266	−0.0625946	−0.0312973	−	0.999510i	$-0.509964\pi$
$103$	−0.635266	−0.0625946	−0.0312973	+	0.999510i	$0.509964\pi$
$104$	−0.478590	−0.0469296
$105$	10.7810	1.05211
$106$	7.92448	0.769694
$107$	−0.308156	−0.0297906	−0.0148953	−	0.999889i	$-0.504741\pi$
$107$	−0.308156	−0.0297906	−0.0148953	+	0.999889i	$0.504741\pi$
$108$	−8.56826	−0.824481
$109$	−10.2283	−0.979698	−0.489849	−	0.871807i	$-0.662948\pi$
$109$	−10.2283	−0.979698	−0.489849	+	0.871807i	$0.662948\pi$
$110$	15.8481	1.51106
$111$	28.9534	2.74814
$112$	1.46435	0.138368
$113$	−16.6320	−1.56461	−0.782304	−	0.622896i	$-0.785956\pi$
$113$	−16.6320	−1.56461	−0.782304	+	0.622896i	$0.785956\pi$
$114$	15.4222	1.44442
$115$	−0.945340	−0.0881534
$116$	−2.45914	−0.228326
$117$	2.81218	0.259986
$118$	−12.9777	−1.19469
$119$	−3.70788	−0.339901
$120$	−7.36226	−0.672080
$121$	30.1288	2.73899
$122$	−0.0523156	−0.00473643
$123$	−23.4234	−2.11201
$124$	−7.92354	−0.711555
$125$	9.62102	0.860530
$126$	−8.60450	−0.766550
$127$	−10.5756	−0.938437	−0.469219	−	0.883082i	$-0.655464\pi$
$127$	−10.5756	−0.938437	−0.469219	+	0.883082i	$0.655464\pi$
$128$	−1.00000	−0.0883883
$129$	3.40211	0.299539
$130$	1.18268	0.103728
$131$	0.149942	0.0131005	0.00655025	−	0.999979i	$-0.497915\pi$
$131$	0.149942	0.0131005	0.00655025	+	0.999979i	$0.497915\pi$
$132$	−19.1065	−1.66301
$133$	7.58026	0.657292
$134$	12.0780	1.04338
$135$	21.1737	1.82234
$136$	2.53209	0.217125
$137$	20.2300	1.72836	0.864181	−	0.503182i	$-0.167837\pi$
$137$	20.2300	1.72836	0.864181	+	0.503182i	$0.167837\pi$
$138$	1.13971	0.0970181
$139$	16.9212	1.43524	0.717618	−	0.696436i	$-0.245232\pi$
$139$	16.9212	1.43524	0.717618	+	0.696436i	$0.245232\pi$
$140$	−3.61867	−0.305834
$141$	−12.0068	−1.01116
$142$	11.7843	0.988917
$143$	3.06928	0.256666
$144$	5.87597	0.489664
$145$	6.07697	0.504665
$146$	−8.80716	−0.728886
$147$	14.4663	1.19316
$148$	−9.71833	−0.798842
$149$	3.59315	0.294362	0.147181	−	0.989110i	$-0.452980\pi$
$149$	3.59315	0.294362	0.147181	+	0.989110i	$0.452980\pi$
$150$	3.29715	0.269211
$151$	17.2013	1.39983	0.699913	−	0.714228i	$-0.253222\pi$
$151$	17.2013	1.39983	0.699913	+	0.714228i	$0.253222\pi$
$152$	−5.17652	−0.419871
$153$	−14.8785	−1.20285
$154$	−9.39116	−0.756761
$155$	19.5805	1.57274
$156$	−1.42584	−0.114159
$157$	−17.6129	−1.40566	−0.702831	−	0.711357i	$-0.748081\pi$
$157$	−17.6129	−1.40566	−0.702831	+	0.711357i	$0.748081\pi$
$158$	−15.4565	−1.22965
$159$	23.6091	1.87232
$160$	2.47117	0.195363
$161$	0.560184	0.0441487
$162$	−7.89912	−0.620613
$163$	−19.4255	−1.52152	−0.760760	−	0.649034i	$-0.775173\pi$
$163$	−19.4255	−1.52152	−0.760760	+	0.649034i	$0.775173\pi$
$164$	7.86215	0.613931
$165$	47.2155	3.67572
$166$	−7.15355	−0.555223
$167$	−14.7386	−1.14051	−0.570255	−	0.821468i	$-0.693155\pi$
$167$	−14.7386	−1.14051	−0.570255	+	0.821468i	$0.693155\pi$
$168$	4.36269	0.336589
$169$	−12.7710	−0.982381
$170$	−6.25724	−0.479908
$171$	30.4171	2.32605
$172$	−1.14193	−0.0870715
$173$	−3.20797	−0.243898	−0.121949	−	0.992536i	$-0.538914\pi$
$173$	−3.20797	−0.243898	−0.121949	+	0.992536i	$0.538914\pi$
$174$	−7.32642	−0.555414
$175$	1.62060	0.122506
$176$	6.41318	0.483411
$177$	−38.6638	−2.90615
$178$	18.0098	1.34989
$179$	0.908856	0.0679311	0.0339655	−	0.999423i	$-0.489186\pi$
$179$	0.908856	0.0679311	0.0339655	+	0.999423i	$0.489186\pi$
$180$	−14.5205	−1.08230
$181$	−9.80983	−0.729159	−0.364580	−	0.931172i	$-0.618787\pi$
$181$	−9.80983	−0.729159	−0.364580	+	0.931172i	$0.618787\pi$
$182$	−0.700826	−0.0519487
$183$	−0.155862	−0.0115216
$184$	−0.382547	−0.0282017
$185$	24.0157	1.76567
$186$	−23.6063	−1.73090
$187$	−16.2387	−1.18749
$188$	4.03015	0.293929
$189$	−12.5470	−0.912657
$190$	12.7921	0.928035
$191$	−8.65733	−0.626423	−0.313211	−	0.949683i	$-0.601405\pi$
$191$	−8.65733	−0.626423	−0.313211	+	0.949683i	$0.601405\pi$
$192$	−2.97926	−0.215009
$193$	−25.6743	−1.84808	−0.924038	−	0.382301i	$-0.875132\pi$
$193$	−25.6743	−1.84808	−0.924038	+	0.382301i	$0.875132\pi$
$194$	−8.49856	−0.610161
$195$	3.52351	0.252324
$196$	−4.85567	−0.346833
$197$	18.1423	1.29259	0.646294	−	0.763089i	$-0.276318\pi$
$197$	18.1423	1.29259	0.646294	+	0.763089i	$0.276318\pi$
$198$	−37.6836	−2.67806
$199$	−24.4995	−1.73672	−0.868361	−	0.495932i	$-0.834827\pi$
$199$	−24.4995	−1.73672	−0.868361	+	0.495932i	$0.834827\pi$
$200$	−1.10670	−0.0782557
$201$	35.9833	2.53807
$202$	−1.37483	−0.0967327
$203$	−3.60106	−0.252745
$204$	7.54375	0.528168
$205$	−19.4287	−1.35696
$206$	0.635266	0.0442611
$207$	2.24783	0.156235
$208$	0.478590	0.0331843
$209$	33.1979	2.29635
$210$	−10.7810	−0.743957
$211$	5.63551	0.387964	0.193982	−	0.981005i	$-0.437860\pi$
$211$	5.63551	0.387964	0.193982	+	0.981005i	$0.437860\pi$
$212$	−7.92448	−0.544256
$213$	35.1085	2.40559
$214$	0.308156	0.0210651
$215$	2.82191	0.192453
$216$	8.56826	0.582996
$217$	−11.6029	−0.787654
$218$	10.2283	0.692751
$219$	−26.2388	−1.77305
$220$	−15.8481	−1.06848
$221$	−1.21183	−0.0815168
$222$	−28.9534	−1.94323
$223$	14.9300	0.999786	0.499893	−	0.866087i	$-0.333373\pi$
$223$	14.9300	0.999786	0.499893	+	0.866087i	$0.333373\pi$
$224$	−1.46435	−0.0978413
$225$	6.50295	0.433530
$226$	16.6320	1.10635
$227$	7.95751	0.528158	0.264079	−	0.964501i	$-0.414932\pi$
$227$	7.95751	0.528158	0.264079	+	0.964501i	$0.414932\pi$
$228$	−15.4222	−1.02136
$229$	−18.8118	−1.24312	−0.621558	−	0.783368i	$-0.713500\pi$
$229$	−18.8118	−1.24312	−0.621558	+	0.783368i	$0.713500\pi$
$230$	0.945340	0.0623339
$231$	−27.9787	−1.84086
$232$	2.45914	0.161451
$233$	25.4066	1.66444	0.832221	−	0.554444i	$-0.187069\pi$
$233$	25.4066	1.66444	0.832221	+	0.554444i	$0.187069\pi$
$234$	−2.81218	−0.183838
$235$	−9.95920	−0.649667
$236$	12.9777	0.844775
$237$	−46.0489	−2.99120
$238$	3.70788	0.240346
$239$	−2.25942	−0.146150	−0.0730750	−	0.997326i	$-0.523281\pi$
$239$	−2.25942	−0.146150	−0.0730750	+	0.997326i	$0.523281\pi$
$240$	7.36226	0.475232
$241$	3.98648	0.256792	0.128396	−	0.991723i	$-0.459017\pi$
$241$	3.98648	0.256792	0.128396	+	0.991723i	$0.459017\pi$
$242$	−30.1288	−1.93676
$243$	2.17126	0.139286
$244$	0.0523156	0.00334917
$245$	11.9992	0.766601
$246$	23.4234	1.49342
$247$	2.47743	0.157635
$248$	7.92354	0.503146
$249$	−21.3123	−1.35061
$250$	−9.62102	−0.608486
$251$	−3.03642	−0.191657	−0.0958285	−	0.995398i	$-0.530550\pi$
$251$	−3.03642	−0.191657	−0.0958285	+	0.995398i	$0.530550\pi$
$252$	8.60450	0.542033
$253$	2.45334	0.154240
$254$	10.5756	0.663575
$255$	−18.6419	−1.16740
$256$	1.00000	0.0625000
$257$	19.4128	1.21094	0.605470	−	0.795868i	$-0.292985\pi$
$257$	19.4128	1.21094	0.605470	+	0.795868i	$0.292985\pi$
$258$	−3.40211	−0.211806
$259$	−14.2311	−0.884276
$260$	−1.18268	−0.0733467
$261$	−14.4499	−0.894423
$262$	−0.149942	−0.00926345
$263$	−3.47046	−0.213998	−0.106999	−	0.994259i	$-0.534124\pi$
$263$	−3.47046	−0.213998	−0.106999	+	0.994259i	$0.534124\pi$
$264$	19.1065	1.17592
$265$	19.5828	1.20296
$266$	−7.58026	−0.464775
$267$	53.6558	3.28368
$268$	−12.0780	−0.737779
$269$	26.4769	1.61433	0.807163	−	0.590329i	$-0.201002\pi$
$269$	26.4769	1.61433	0.807163	+	0.590329i	$0.201002\pi$
$270$	−21.1737	−1.28859
$271$	4.40055	0.267314	0.133657	−	0.991028i	$-0.457328\pi$
$271$	4.40055	0.267314	0.133657	+	0.991028i	$0.457328\pi$
$272$	−2.53209	−0.153531
$273$	−2.08794	−0.126368
$274$	−20.2300	−1.22214
$275$	7.09748	0.427994
$276$	−1.13971	−0.0686022
$277$	−12.3546	−0.742316	−0.371158	−	0.928570i	$-0.621039\pi$
$277$	−12.3546	−0.742316	−0.371158	+	0.928570i	$0.621039\pi$
$278$	−16.9212	−1.01487
$279$	−46.5585	−2.78739
$280$	3.61867	0.216257
$281$	−25.1724	−1.50166	−0.750828	−	0.660497i	$-0.770345\pi$
$281$	−25.1724	−1.50166	−0.750828	+	0.660497i	$0.770345\pi$
$282$	12.0068	0.714997
$283$	−15.7388	−0.935576	−0.467788	−	0.883841i	$-0.654949\pi$
$283$	−15.7388	−0.935576	−0.467788	+	0.883841i	$0.654949\pi$
$284$	−11.7843	−0.699270
$285$	38.1109	2.25749
$286$	−3.06928	−0.181491
$287$	11.5130	0.679589
$288$	−5.87597	−0.346245
$289$	−10.5885	−0.622854
$290$	−6.07697	−0.356852
$291$	−25.3194	−1.48425
$292$	8.80716	0.515400
$293$	23.5265	1.37443	0.687216	−	0.726453i	$-0.258833\pi$
$293$	23.5265	1.37443	0.687216	+	0.726453i	$0.258833\pi$
$294$	−14.4663	−0.843691
$295$	−32.0701	−1.86719
$296$	9.71833	0.564867
$297$	−54.9497	−3.18851
$298$	−3.59315	−0.208146
$299$	0.183083	0.0105880
$300$	−3.29715	−0.190361
$301$	−1.67219	−0.0963836
$302$	−17.2013	−0.989826
$303$	−4.09597	−0.235307
$304$	5.17652	0.296894
$305$	−0.129281	−0.00740261
$306$	14.8785	0.850547
$307$	−6.82603	−0.389582	−0.194791	−	0.980845i	$-0.562403\pi$
$307$	−6.82603	−0.389582	−0.194791	+	0.980845i	$0.562403\pi$
$308$	9.39116	0.535111
$309$	1.89262	0.107667
$310$	−19.5805	−1.11210
$311$	−11.5412	−0.654439	−0.327220	−	0.944948i	$-0.606112\pi$
$311$	−11.5412	−0.654439	−0.327220	+	0.944948i	$0.606112\pi$
$312$	1.42584	0.0807225
$313$	26.1314	1.47703	0.738517	−	0.674235i	$-0.235527\pi$
$313$	26.1314	1.47703	0.738517	+	0.674235i	$0.235527\pi$
$314$	17.6129	0.993953
$315$	−21.2632	−1.19805
$316$	15.4565	0.869496
$317$	33.1234	1.86040	0.930198	−	0.367059i	$-0.119635\pi$
$317$	33.1234	1.86040	0.930198	+	0.367059i	$0.119635\pi$
$318$	−23.6091	−1.32393
$319$	−15.7709	−0.883002
$320$	−2.47117	−0.138143
$321$	0.918076	0.0512420
$322$	−0.560184	−0.0312178
$323$	−13.1074	−0.729316
$324$	7.89912	0.438840
$325$	0.529657	0.0293801
$326$	19.4255	1.07588
$327$	30.4729	1.68515
$328$	−7.86215	−0.434114
$329$	5.90156	0.325364
$330$	−47.2155	−2.59913
$331$	−0.975324	−0.0536086	−0.0268043	−	0.999641i	$-0.508533\pi$
$331$	−0.975324	−0.0536086	−0.0268043	+	0.999641i	$0.508533\pi$
$332$	7.15355	0.392602
$333$	−57.1046	−3.12932
$334$	14.7386	0.806462
$335$	29.8467	1.63070
$336$	−4.36269	−0.238004
$337$	−29.2572	−1.59374	−0.796871	−	0.604149i	$-0.793513\pi$
$337$	−29.2572	−1.59374	−0.796871	+	0.604149i	$0.793513\pi$
$338$	12.7710	0.694648
$339$	49.5511	2.69124
$340$	6.25724	0.339346
$341$	−50.8151	−2.75179
$342$	−30.4171	−1.64477
$343$	−17.3609	−0.937400
$344$	1.14193	0.0615689
$345$	2.81641	0.151630
$346$	3.20797	0.172462
$347$	5.41803	0.290855	0.145427	−	0.989369i	$-0.453544\pi$
$347$	5.41803	0.290855	0.145427	+	0.989369i	$0.453544\pi$
$348$	7.32642	0.392737
$349$	0.281385	0.0150622	0.00753110	−	0.999972i	$-0.497603\pi$
$349$	0.281385	0.0150622	0.00753110	+	0.999972i	$0.497603\pi$
$350$	−1.62060	−0.0866250
$351$	−4.10068	−0.218878
$352$	−6.41318	−0.341823
$353$	14.2346	0.757632	0.378816	−	0.925472i	$-0.376331\pi$
$353$	14.2346	0.757632	0.378816	+	0.925472i	$0.376331\pi$
$354$	38.6638	2.05496
$355$	29.1211	1.54559
$356$	−18.0098	−0.954517
$357$	11.0467	0.584654
$358$	−0.908856	−0.0480345
$359$	−31.6269	−1.66920	−0.834601	−	0.550855i	$-0.814302\pi$
$359$	−31.6269	−1.66920	−0.834601	+	0.550855i	$0.814302\pi$
$360$	14.5205	0.765300
$361$	7.79635	0.410334
$362$	9.80983	0.515593
$363$	−89.7616	−4.71126
$364$	0.700826	0.0367332
$365$	−21.7640	−1.13918
$366$	0.155862	0.00814702
$367$	14.8173	0.773455	0.386728	−	0.922194i	$-0.373605\pi$
$367$	14.8173	0.773455	0.386728	+	0.922194i	$0.373605\pi$
$368$	0.382547	0.0199416
$369$	46.1977	2.40496
$370$	−24.0157	−1.24852
$371$	−11.6042	−0.602462
$372$	23.6063	1.22393
$373$	−26.1139	−1.35213	−0.676064	−	0.736842i	$-0.736316\pi$
$373$	−26.1139	−1.35213	−0.676064	+	0.736842i	$0.736316\pi$
$374$	16.2387	0.839686
$375$	−28.6635	−1.48018
$376$	−4.03015	−0.207839
$377$	−1.17692	−0.0606146
$378$	12.5470	0.645346
$379$	24.4126	1.25399	0.626995	−	0.779023i	$-0.284285\pi$
$379$	24.4126	1.25399	0.626995	+	0.779023i	$0.284285\pi$
$380$	−12.7921	−0.656220
$381$	31.5076	1.61418
$382$	8.65733	0.442948
$383$	−32.2739	−1.64912	−0.824560	−	0.565775i	$-0.808577\pi$
$383$	−32.2739	−1.64912	−0.824560	+	0.565775i	$0.808577\pi$
$384$	2.97926	0.152035
$385$	−23.2072	−1.18275
$386$	25.6743	1.30679
$387$	−6.70996	−0.341087
$388$	8.49856	0.431449
$389$	7.19662	0.364883	0.182442	−	0.983217i	$-0.441600\pi$
$389$	7.19662	0.364883	0.182442	+	0.983217i	$0.441600\pi$
$390$	−3.52351	−0.178420
$391$	−0.968643	−0.0489864
$392$	4.85567	0.245248
$393$	−0.446716	−0.0225338
$394$	−18.1423	−0.913997
$395$	−38.1957	−1.92184
$396$	37.6836	1.89367
$397$	−6.14482	−0.308400	−0.154200	−	0.988040i	$-0.549280\pi$
$397$	−6.14482	−0.308400	−0.154200	+	0.988040i	$0.549280\pi$
$398$	24.4995	1.22805
$399$	−22.5835	−1.13059
$400$	1.10670	0.0553351
$401$	2.62901	0.131286	0.0656432	−	0.997843i	$-0.479090\pi$
$401$	2.62901	0.131286	0.0656432	+	0.997843i	$0.479090\pi$
$402$	−35.9833	−1.79469
$403$	−3.79213	−0.188900
$404$	1.37483	0.0684003
$405$	−19.5201	−0.969962
$406$	3.60106	0.178717
$407$	−62.3254	−3.08936
$408$	−7.54375	−0.373471
$409$	−9.50622	−0.470052	−0.235026	−	0.971989i	$-0.575518\pi$
$409$	−9.50622	−0.470052	−0.235026	+	0.971989i	$0.575518\pi$
$410$	19.4287	0.959517
$411$	−60.2702	−2.97291
$412$	−0.635266	−0.0312973
$413$	19.0039	0.935121
$414$	−2.24783	−0.110475
$415$	−17.6777	−0.867762
$416$	−0.478590	−0.0234648
$417$	−50.4126	−2.46871
$418$	−33.1979	−1.62376
$419$	16.3874	0.800575	0.400288	−	0.916390i	$-0.368910\pi$
$419$	16.3874	0.800575	0.400288	+	0.916390i	$0.368910\pi$
$420$	10.7810	0.526057
$421$	−6.89917	−0.336245	−0.168122	−	0.985766i	$-0.553770\pi$
$421$	−6.89917	−0.336245	−0.168122	+	0.985766i	$0.553770\pi$
$422$	−5.63551	−0.274332
$423$	23.6810	1.15141
$424$	7.92448	0.384847
$425$	−2.80227	−0.135930
$426$	−35.1085	−1.70101
$427$	0.0766086	0.00370735
$428$	−0.308156	−0.0148953
$429$	−9.14419	−0.441486
$430$	−2.82191	−0.136085
$431$	−24.5585	−1.18294	−0.591471	−	0.806326i	$-0.701453\pi$
$431$	−24.5585	−1.18294	−0.591471	+	0.806326i	$0.701453\pi$
$432$	−8.56826	−0.412240
$433$	−3.33798	−0.160413	−0.0802066	−	0.996778i	$-0.525558\pi$
$433$	−3.33798	−0.160413	−0.0802066	+	0.996778i	$0.525558\pi$
$434$	11.6029	0.556956
$435$	−18.1049	−0.868061
$436$	−10.2283	−0.489849
$437$	1.98026	0.0947287
$438$	26.2388	1.25374
$439$	−19.1932	−0.916039	−0.458020	−	0.888942i	$-0.651441\pi$
$439$	−19.1932	−0.916039	−0.458020	+	0.888942i	$0.651441\pi$
$440$	15.8481	0.755528
$441$	−28.5318	−1.35866
$442$	1.21183	0.0576411
$443$	21.3619	1.01493	0.507467	−	0.861671i	$-0.330582\pi$
$443$	21.3619	1.01493	0.507467	+	0.861671i	$0.330582\pi$
$444$	28.9534	1.37407
$445$	44.5053	2.10975
$446$	−14.9300	−0.706956
$447$	−10.7049	−0.506325
$448$	1.46435	0.0691842
$449$	−24.8314	−1.17186	−0.585932	−	0.810360i	$-0.699272\pi$
$449$	−24.8314	−1.17186	−0.585932	+	0.810360i	$0.699272\pi$
$450$	−6.50295	−0.306552
$451$	50.4213	2.37425
$452$	−16.6320	−0.782304
$453$	−51.2472	−2.40780
$454$	−7.95751	−0.373464
$455$	−1.73186	−0.0811910
$456$	15.4222	0.722210
$457$	2.67559	0.125159	0.0625794	−	0.998040i	$-0.480067\pi$
$457$	2.67559	0.125159	0.0625794	+	0.998040i	$0.480067\pi$
$458$	18.8118	0.879016
$459$	21.6956	1.01266
$460$	−0.945340	−0.0440767
$461$	0.824305	0.0383917	0.0191959	−	0.999816i	$-0.493889\pi$
$461$	0.824305	0.0383917	0.0191959	+	0.999816i	$0.493889\pi$
$462$	27.9787	1.30169
$463$	−2.14353	−0.0996181	−0.0498091	−	0.998759i	$-0.515861\pi$
$463$	−2.14353	−0.0996181	−0.0498091	+	0.998759i	$0.515861\pi$
$464$	−2.45914	−0.114163
$465$	−58.3352	−2.70523
$466$	−25.4066	−1.17694
$467$	−5.09071	−0.235570	−0.117785	−	0.993039i	$-0.537579\pi$
$467$	−5.09071	−0.235570	−0.117785	+	0.993039i	$0.537579\pi$
$468$	2.81218	0.129993
$469$	−17.6864	−0.816682
$470$	9.95920	0.459384
$471$	52.4733	2.41784
$472$	−12.9777	−0.597346
$473$	−7.32341	−0.336731
$474$	46.0489	2.11510
$475$	5.72887	0.262859
$476$	−3.70788	−0.169950
$477$	−46.5640	−2.13202
$478$	2.25942	0.103344
$479$	0.418048	0.0191011	0.00955056	−	0.999954i	$-0.496960\pi$
$479$	0.418048	0.0191011	0.00955056	+	0.999954i	$0.496960\pi$
$480$	−7.36226	−0.336040
$481$	−4.65110	−0.212072
$482$	−3.98648	−0.181579
$483$	−1.66893	−0.0759390
$484$	30.1288	1.36949
$485$	−21.0014	−0.953625
$486$	−2.17126	−0.0984904
$487$	30.1218	1.36495	0.682475	−	0.730909i	$-0.260904\pi$
$487$	30.1218	1.36495	0.682475	+	0.730909i	$0.260904\pi$
$488$	−0.0523156	−0.00236822
$489$	57.8734	2.61713
$490$	−11.9992	−0.542069
$491$	41.8209	1.88735	0.943675	−	0.330874i	$-0.107343\pi$
$491$	41.8209	1.88735	0.943675	+	0.330874i	$0.107343\pi$
$492$	−23.4234	−1.05601
$493$	6.22677	0.280440
$494$	−2.47743	−0.111465
$495$	−93.1228	−4.18556
$496$	−7.92354	−0.355778
$497$	−17.2564	−0.774055
$498$	21.3123	0.955025
$499$	−16.5086	−0.739025	−0.369513	−	0.929226i	$-0.620475\pi$
$499$	−16.5086	−0.739025	−0.369513	+	0.929226i	$0.620475\pi$
$500$	9.62102	0.430265
$501$	43.9101	1.96176
$502$	3.03642	0.135522
$503$	−25.8773	−1.15381	−0.576906	−	0.816811i	$-0.695740\pi$
$503$	−25.8773	−1.15381	−0.576906	+	0.816811i	$0.695740\pi$
$504$	−8.60450	−0.383275
$505$	−3.39744	−0.151184
$506$	−2.45334	−0.109064
$507$	38.0479	1.68977
$508$	−10.5756	−0.469219
$509$	3.93326	0.174339	0.0871694	−	0.996194i	$-0.472218\pi$
$509$	3.93326	0.174339	0.0871694	+	0.996194i	$0.472218\pi$
$510$	18.6419	0.825478
$511$	12.8968	0.570521
$512$	−1.00000	−0.0441942
$513$	−44.3537	−1.95827
$514$	−19.4128	−0.856264
$515$	1.56985	0.0691760
$516$	3.40211	0.149770
$517$	25.8461	1.13671
$518$	14.2311	0.625278
$519$	9.55738	0.419522
$520$	1.18268	0.0518640
$521$	0.166899	0.00731197	0.00365599	−	0.999993i	$-0.498836\pi$
$521$	0.166899	0.00731197	0.00365599	+	0.999993i	$0.498836\pi$
$522$	14.4499	0.632453
$523$	0.467108	0.0204252	0.0102126	−	0.999948i	$-0.496749\pi$
$523$	0.467108	0.0204252	0.0102126	+	0.999948i	$0.496749\pi$
$524$	0.149942	0.00655025
$525$	−4.82820	−0.210720
$526$	3.47046	0.151319
$527$	20.0631	0.873964
$528$	−19.1065	−0.831504
$529$	−22.8537	−0.993637
$530$	−19.5828	−0.850621
$531$	76.2564	3.30925
$532$	7.58026	0.328646
$533$	3.76275	0.162983
$534$	−53.6558	−2.32191
$535$	0.761507	0.0329228
$536$	12.0780	0.521688
$537$	−2.70771	−0.116846
$538$	−26.4769	−1.14150
$539$	−31.1403	−1.34131
$540$	21.1737	0.911169
$541$	28.5813	1.22881	0.614403	−	0.788993i	$-0.289397\pi$
$541$	28.5813	1.22881	0.614403	+	0.788993i	$0.289397\pi$
$542$	−4.40055	−0.189020
$543$	29.2260	1.25421
$544$	2.53209	0.108563
$545$	25.2760	1.08271
$546$	2.08794	0.0893556
$547$	−24.8529	−1.06263	−0.531317	−	0.847173i	$-0.678303\pi$
$547$	−24.8529	−1.06263	−0.531317	+	0.847173i	$0.678303\pi$
$548$	20.2300	0.864181
$549$	0.307405	0.0131197
$550$	−7.09748	−0.302638
$551$	−12.7298	−0.542308
$552$	1.13971	0.0485091
$553$	22.6338	0.962487
$554$	12.3546	0.524897
$555$	−71.5489	−3.03708
$556$	16.9212	0.717618
$557$	40.1900	1.70291	0.851453	−	0.524432i	$-0.175722\pi$
$557$	40.1900	1.70291	0.851453	+	0.524432i	$0.175722\pi$
$558$	46.5585	1.97098
$559$	−0.546518	−0.0231152
$560$	−3.61867	−0.152917
$561$	48.3794	2.04258
$562$	25.1724	1.06183
$563$	−44.2290	−1.86403	−0.932015	−	0.362420i	$-0.881951\pi$
$563$	−44.2290	−1.86403	−0.932015	+	0.362420i	$0.881951\pi$
$564$	−12.0068	−0.505579
$565$	41.1006	1.72912
$566$	15.7388	0.661552
$567$	11.5671	0.485773
$568$	11.7843	0.494459
$569$	14.1281	0.592281	0.296141	−	0.955144i	$-0.404300\pi$
$569$	14.1281	0.592281	0.296141	+	0.955144i	$0.404300\pi$
$570$	−38.1109	−1.59629
$571$	35.2674	1.47589	0.737947	−	0.674859i	$-0.235795\pi$
$571$	35.2674	1.47589	0.737947	+	0.674859i	$0.235795\pi$
$572$	3.06928	0.128333
$573$	25.7924	1.07749
$574$	−11.5130	−0.480542
$575$	0.423366	0.0176556
$576$	5.87597	0.244832
$577$	−5.50115	−0.229016	−0.114508	−	0.993422i	$-0.536529\pi$
$577$	−5.50115	−0.229016	−0.114508	+	0.993422i	$0.536529\pi$
$578$	10.5885	0.440424
$579$	76.4903	3.17883
$580$	6.07697	0.252332
$581$	10.4753	0.434590
$582$	25.3194	1.04952
$583$	−50.8211	−2.10479
$584$	−8.80716	−0.364443
$585$	−6.94939	−0.287322
$586$	−23.5265	−0.971870
$587$	−43.2238	−1.78404	−0.892019	−	0.451997i	$-0.850712\pi$
$587$	−43.2238	−1.78404	−0.892019	+	0.451997i	$0.850712\pi$
$588$	14.4663	0.596579
$589$	−41.0164	−1.69005
$590$	32.0701	1.32031
$591$	−54.0507	−2.22335
$592$	−9.71833	−0.399421
$593$	−4.41600	−0.181343	−0.0906717	−	0.995881i	$-0.528901\pi$
$593$	−4.41600	−0.181343	−0.0906717	+	0.995881i	$0.528901\pi$
$594$	54.9497	2.25462
$595$	9.16281	0.375639
$596$	3.59315	0.147181
$597$	72.9903	2.98729
$598$	−0.183083	−0.00748683
$599$	−7.34795	−0.300229	−0.150115	−	0.988669i	$-0.547964\pi$
$599$	−7.34795	−0.300229	−0.150115	+	0.988669i	$0.547964\pi$
$600$	3.29715	0.134606
$601$	−2.13917	−0.0872587	−0.0436294	−	0.999048i	$-0.513892\pi$
$601$	−2.13917	−0.0872587	−0.0436294	+	0.999048i	$0.513892\pi$
$602$	1.67219	0.0681535
$603$	−70.9697	−2.89011
$604$	17.2013	0.699913
$605$	−74.4536	−3.02697
$606$	4.09597	0.166387
$607$	−34.9139	−1.41711	−0.708557	−	0.705654i	$-0.750653\pi$
$607$	−34.9139	−1.41711	−0.708557	+	0.705654i	$0.750653\pi$
$608$	−5.17652	−0.209936
$609$	10.7285	0.434740
$610$	0.129281	0.00523444
$611$	1.92879	0.0780305
$612$	−14.8785	−0.601427
$613$	−43.8792	−1.77227	−0.886133	−	0.463432i	$-0.846618\pi$
$613$	−43.8792	−1.77227	−0.886133	+	0.463432i	$0.846618\pi$
$614$	6.82603	0.275476
$615$	57.8832	2.33408
$616$	−9.39116	−0.378381
$617$	−32.4566	−1.30665	−0.653327	−	0.757076i	$-0.726627\pi$
$617$	−32.4566	−1.30665	−0.653327	+	0.757076i	$0.726627\pi$
$618$	−1.89262	−0.0761323
$619$	43.3869	1.74387	0.871933	−	0.489625i	$-0.162866\pi$
$619$	43.3869	1.74387	0.871933	+	0.489625i	$0.162866\pi$
$620$	19.5805	0.786370
$621$	−3.27776	−0.131532
$622$	11.5412	0.462758
$623$	−26.3727	−1.05660
$624$	−1.42584	−0.0570794
$625$	−29.3087	−1.17235
$626$	−26.1314	−1.04442
$627$	−98.9052	−3.94989
$628$	−17.6129	−0.702831
$629$	24.6077	0.981174
$630$	21.2632	0.847147
$631$	−8.00318	−0.318601	−0.159301	−	0.987230i	$-0.550924\pi$
$631$	−8.00318	−0.318601	−0.159301	+	0.987230i	$0.550924\pi$
$632$	−15.4565	−0.614827
$633$	−16.7896	−0.667328
$634$	−33.1234	−1.31550
$635$	26.1343	1.03711
$636$	23.6091	0.936160
$637$	−2.32388	−0.0920753
$638$	15.7709	0.624377
$639$	−69.2443	−2.73926
$640$	2.47117	0.0976817
$641$	23.1323	0.913671	0.456835	−	0.889551i	$-0.348983\pi$
$641$	23.1323	0.913671	0.456835	+	0.889551i	$0.348983\pi$
$642$	−0.918076	−0.0362336
$643$	−15.7020	−0.619227	−0.309614	−	0.950862i	$-0.600200\pi$
$643$	−15.7020	−0.619227	−0.309614	+	0.950862i	$0.600200\pi$
$644$	0.560184	0.0220743
$645$	−8.40721	−0.331033
$646$	13.1074	0.515704
$647$	−13.5848	−0.534073	−0.267037	−	0.963686i	$-0.586044\pi$
$647$	−13.5848	−0.534073	−0.267037	+	0.963686i	$0.586044\pi$
$648$	−7.89912	−0.310307
$649$	83.2281	3.26699
$650$	−0.529657	−0.0207749
$651$	34.5679	1.35482
$652$	−19.4255	−0.760760
$653$	33.4183	1.30776	0.653879	−	0.756599i	$-0.273141\pi$
$653$	33.4183	1.30776	0.653879	+	0.756599i	$0.273141\pi$
$654$	−30.4729	−1.19158
$655$	−0.370533	−0.0144779
$656$	7.86215	0.306965
$657$	51.7506	2.01898
$658$	−5.90156	−0.230067
$659$	−9.14279	−0.356153	−0.178076	−	0.984017i	$-0.556987\pi$
$659$	−9.14279	−0.356153	−0.178076	+	0.984017i	$0.556987\pi$
$660$	47.2155	1.83786
$661$	−5.54582	−0.215708	−0.107854	−	0.994167i	$-0.534398\pi$
$661$	−5.54582	−0.215708	−0.107854	+	0.994167i	$0.534398\pi$
$662$	0.975324	0.0379070
$663$	3.61037	0.140215
$664$	−7.15355	−0.277611
$665$	−18.7321	−0.726401
$666$	57.1046	2.21276
$667$	−0.940737	−0.0364255
$668$	−14.7386	−0.570255
$669$	−44.4803	−1.71971
$670$	−29.8467	−1.15308
$671$	0.335509	0.0129522
$672$	4.36269	0.168294
$673$	13.4801	0.519620	0.259810	−	0.965660i	$-0.416340\pi$
$673$	13.4801	0.519620	0.259810	+	0.965660i	$0.416340\pi$
$674$	29.2572	1.12695
$675$	−9.48251	−0.364982
$676$	−12.7710	−0.491190
$677$	33.6462	1.29313	0.646565	−	0.762859i	$-0.276205\pi$
$677$	33.6462	1.29313	0.646565	+	0.762859i	$0.276205\pi$
$678$	−49.5511	−1.90300
$679$	12.4449	0.477591
$680$	−6.25724	−0.239954
$681$	−23.7075	−0.908472
$682$	50.8151	1.94581
$683$	33.7088	1.28983	0.644915	−	0.764254i	$-0.276893\pi$
$683$	33.7088	1.28983	0.644915	+	0.764254i	$0.276893\pi$
$684$	30.4171	1.16303
$685$	−49.9917	−1.91009
$686$	17.3609	0.662842
$687$	56.0451	2.13825
$688$	−1.14193	−0.0435358
$689$	−3.79258	−0.144486
$690$	−2.81641	−0.107219
$691$	−3.70644	−0.141000	−0.0704998	−	0.997512i	$-0.522459\pi$
$691$	−3.70644	−0.141000	−0.0704998	+	0.997512i	$0.522459\pi$
$692$	−3.20797	−0.121949
$693$	55.1822	2.09620
$694$	−5.41803	−0.205665
$695$	−41.8152	−1.58614
$696$	−7.32642	−0.277707
$697$	−19.9077	−0.754057
$698$	−0.281385	−0.0106506
$699$	−75.6928	−2.86296
$700$	1.62060	0.0612531
$701$	−22.3659	−0.844748	−0.422374	−	0.906422i	$-0.638803\pi$
$701$	−22.3659	−0.844748	−0.422374	+	0.906422i	$0.638803\pi$
$702$	4.10068	0.154770
$703$	−50.3071	−1.89737
$704$	6.41318	0.241706
$705$	29.6710	1.11747
$706$	−14.2346	−0.535726
$707$	2.01324	0.0757156
$708$	−38.6638	−1.45308
$709$	38.2167	1.43526	0.717629	−	0.696425i	$-0.245227\pi$
$709$	38.2167	1.43526	0.717629	+	0.696425i	$0.245227\pi$
$710$	−29.1211	−1.09289
$711$	90.8220	3.40609
$712$	18.0098	0.674945
$713$	−3.03113	−0.113517
$714$	−11.0467	−0.413413
$715$	−7.58474	−0.283653
$716$	0.908856	0.0339655
$717$	6.73141	0.251389
$718$	31.6269	1.18030
$719$	19.5944	0.730747	0.365374	−	0.930861i	$-0.380941\pi$
$719$	19.5944	0.730747	0.365374	+	0.930861i	$0.380941\pi$
$720$	−14.5205	−0.541149
$721$	−0.930254	−0.0346445
$722$	−7.79635	−0.290150
$723$	−11.8768	−0.441701
$724$	−9.80983	−0.364580
$725$	−2.72154	−0.101075
$726$	89.7616	3.33136
$727$	−11.8677	−0.440149	−0.220075	−	0.975483i	$-0.570630\pi$
$727$	−11.8677	−0.440149	−0.220075	+	0.975483i	$0.570630\pi$
$728$	−0.700826	−0.0259743
$729$	−30.1661	−1.11726
$730$	21.7640	0.805523
$731$	2.89148	0.106945
$732$	−0.155862	−0.00576081
$733$	−24.3044	−0.897703	−0.448851	−	0.893606i	$-0.648167\pi$
$733$	−24.3044	−0.897703	−0.448851	+	0.893606i	$0.648167\pi$
$734$	−14.8173	−0.546915
$735$	−35.7487	−1.31861
$736$	−0.382547	−0.0141009
$737$	−77.4581	−2.85320
$738$	−46.1977	−1.70056
$739$	−18.8781	−0.694442	−0.347221	−	0.937783i	$-0.612875\pi$
$739$	−18.8781	−0.694442	−0.347221	+	0.937783i	$0.612875\pi$
$740$	24.0157	0.882835
$741$	−7.38091	−0.271144
$742$	11.6042	0.426005
$743$	−44.4788	−1.63177	−0.815885	−	0.578215i	$-0.803750\pi$
$743$	−44.4788	−1.63177	−0.815885	+	0.578215i	$0.803750\pi$
$744$	−23.6063	−0.865448
$745$	−8.87930	−0.325312
$746$	26.1139	0.956100
$747$	42.0340	1.53794
$748$	−16.2387	−0.593747
$749$	−0.451249	−0.0164883
$750$	28.6635	1.04664
$751$	−14.8724	−0.542703	−0.271351	−	0.962480i	$-0.587471\pi$
$751$	−14.8724	−0.542703	−0.271351	+	0.962480i	$0.587471\pi$
$752$	4.03015	0.146964
$753$	9.04627	0.329664
$754$	1.17692	0.0428610
$755$	−42.5075	−1.54701
$756$	−12.5470	−0.456328
$757$	30.2846	1.10071	0.550356	−	0.834930i	$-0.314492\pi$
$757$	30.2846	1.10071	0.550356	+	0.834930i	$0.314492\pi$
$758$	−24.4126	−0.886705
$759$	−7.30913	−0.265305
$760$	12.7921	0.464018
$761$	−23.4928	−0.851613	−0.425806	−	0.904814i	$-0.640009\pi$
$761$	−23.4928	−0.851613	−0.425806	+	0.904814i	$0.640009\pi$
$762$	−31.5076	−1.14140
$763$	−14.9779	−0.542237
$764$	−8.65733	−0.313211
$765$	36.7674	1.32933
$766$	32.2739	1.16610
$767$	6.21099	0.224266
$768$	−2.97926	−0.107505
$769$	5.37079	0.193676	0.0968379	−	0.995300i	$-0.469127\pi$
$769$	5.37079	0.193676	0.0968379	+	0.995300i	$0.469127\pi$
$770$	23.2072	0.836329
$771$	−57.8358	−2.08291
$772$	−25.6743	−0.924038
$773$	18.1983	0.654549	0.327274	−	0.944929i	$-0.393870\pi$
$773$	18.1983	0.654549	0.327274	+	0.944929i	$0.393870\pi$
$774$	6.70996	0.241185
$775$	−8.76901	−0.314992
$776$	−8.49856	−0.305081
$777$	42.3980	1.52102
$778$	−7.19662	−0.258011
$779$	40.6986	1.45818
$780$	3.52351	0.126162
$781$	−75.5749	−2.70428
$782$	0.968643	0.0346386
$783$	21.0706	0.753001
$784$	−4.85567	−0.173417
$785$	43.5245	1.55346
$786$	0.446716	0.0159338
$787$	−40.1709	−1.43194	−0.715968	−	0.698133i	$-0.754015\pi$
$787$	−40.1709	−1.43194	−0.715968	+	0.698133i	$0.754015\pi$
$788$	18.1423	0.646294
$789$	10.3394	0.368092
$790$	38.1957	1.35894
$791$	−24.3552	−0.865970
$792$	−37.6836	−1.33903
$793$	0.0250378	0.000889117 0
$794$	6.14482	0.218072
$795$	−58.3421	−2.06918
$796$	−24.4995	−0.868361
$797$	27.3769	0.969741	0.484871	−	0.874586i	$-0.338867\pi$
$797$	27.3769	0.969741	0.484871	+	0.874586i	$0.338867\pi$
$798$	22.5835	0.799448
$799$	−10.2047	−0.361016
$800$	−1.10670	−0.0391279
$801$	−105.825	−3.73914
$802$	−2.62901	−0.0928335
$803$	56.4819	1.99320
$804$	35.9833	1.26903
$805$	−1.38431	−0.0487906
$806$	3.79213	0.133572
$807$	−78.8815	−2.77676
$808$	−1.37483	−0.0483664
$809$	−28.9799	−1.01888	−0.509440	−	0.860506i	$-0.670147\pi$
$809$	−28.9799	−1.01888	−0.509440	+	0.860506i	$0.670147\pi$
$810$	19.5201	0.685866
$811$	12.2552	0.430338	0.215169	−	0.976577i	$-0.430970\pi$
$811$	12.2552	0.430338	0.215169	+	0.976577i	$0.430970\pi$
$812$	−3.60106	−0.126372
$813$	−13.1104	−0.459800
$814$	62.3254	2.18450
$815$	48.0037	1.68150
$816$	7.54375	0.264084
$817$	−5.91123	−0.206808
$818$	9.50622	0.332377
$819$	4.11803	0.143896
$820$	−19.4287	−0.678481
$821$	−31.0442	−1.08345	−0.541725	−	0.840556i	$-0.682229\pi$
$821$	−31.0442	−1.08345	−0.541725	+	0.840556i	$0.682229\pi$
$822$	60.2702	2.10217
$823$	−6.44240	−0.224568	−0.112284	−	0.993676i	$-0.535817\pi$
$823$	−6.44240	−0.224568	−0.112284	+	0.993676i	$0.535817\pi$
$824$	0.635266	0.0221305
$825$	−21.1452	−0.736182
$826$	−19.0039	−0.661231
$827$	11.7834	0.409750	0.204875	−	0.978788i	$-0.434321\pi$
$827$	11.7834	0.409750	0.204875	+	0.978788i	$0.434321\pi$
$828$	2.24783	0.0781176
$829$	−22.2206	−0.771754	−0.385877	−	0.922550i	$-0.626101\pi$
$829$	−22.2206	−0.771754	−0.385877	+	0.922550i	$0.626101\pi$
$830$	17.6777	0.613601
$831$	36.8075	1.27684
$832$	0.478590	0.0165921
$833$	12.2950	0.425996
$834$	50.4126	1.74564
$835$	36.4217	1.26043
$836$	33.1979	1.14817
$837$	67.8910	2.34665
$838$	−16.3874	−0.566092
$839$	−32.6893	−1.12856	−0.564281	−	0.825583i	$-0.690846\pi$
$839$	−32.6893	−1.12856	−0.564281	+	0.825583i	$0.690846\pi$
$840$	−10.7810	−0.371978
$841$	−22.9526	−0.791470
$842$	6.89917	0.237761
$843$	74.9949	2.58296
$844$	5.63551	0.193982
$845$	31.5592	1.08567
$846$	−23.6810	−0.814171
$847$	44.1193	1.51596
$848$	−7.92448	−0.272128
$849$	46.8900	1.60926
$850$	2.80227	0.0961172
$851$	−3.71772	−0.127442
$852$	35.1085	1.20280
$853$	−5.06104	−0.173287	−0.0866433	−	0.996239i	$-0.527614\pi$
$853$	−5.06104	−0.173287	−0.0866433	+	0.996239i	$0.527614\pi$
$854$	−0.0766086	−0.00262149
$855$	−75.1659	−2.57062
$856$	0.308156	0.0105326
$857$	0.956262	0.0326653	0.0163326	−	0.999867i	$-0.494801\pi$
$857$	0.956262	0.0326653	0.0163326	+	0.999867i	$0.494801\pi$
$858$	9.14419	0.312177
$859$	29.5356	1.00774	0.503871	−	0.863779i	$-0.331909\pi$
$859$	29.5356	1.00774	0.503871	+	0.863779i	$0.331909\pi$
$860$	2.82191	0.0962265
$861$	−34.3001	−1.16894
$862$	24.5585	0.836466
$863$	−5.36642	−0.182675	−0.0913375	−	0.995820i	$-0.529114\pi$
$863$	−5.36642	−0.182675	−0.0913375	+	0.995820i	$0.529114\pi$
$864$	8.56826	0.291498
$865$	7.92746	0.269542
$866$	3.33798	0.113429
$867$	31.5459	1.07136
$868$	−11.6029	−0.393827
$869$	99.1253	3.36260
$870$	18.1049	0.613812
$871$	−5.78039	−0.195861
$872$	10.2283	0.346375
$873$	49.9373	1.69012
$874$	−1.98026	−0.0669833
$875$	14.0886	0.476281
$876$	−26.2388	−0.886527
$877$	33.5566	1.13313	0.566564	−	0.824018i	$-0.308273\pi$
$877$	33.5566	1.13313	0.566564	+	0.824018i	$0.308273\pi$
$878$	19.1932	0.647738
$879$	−70.0914	−2.36413
$880$	−15.8481	−0.534239
$881$	−10.1130	−0.340717	−0.170358	−	0.985382i	$-0.554493\pi$
$881$	−10.1130	−0.340717	−0.170358	+	0.985382i	$0.554493\pi$
$882$	28.5318	0.960714
$883$	−27.6207	−0.929510	−0.464755	−	0.885439i	$-0.653858\pi$
$883$	−27.6207	−0.929510	−0.464755	+	0.885439i	$0.653858\pi$
$884$	−1.21183	−0.0407584
$885$	95.5451	3.21171
$886$	−21.3619	−0.717667
$887$	−48.5938	−1.63162	−0.815810	−	0.578320i	$-0.803709\pi$
$887$	−48.5938	−1.63162	−0.815810	+	0.578320i	$0.803709\pi$
$888$	−28.9534	−0.971613
$889$	−15.4865	−0.519400
$890$	−44.5053	−1.49182
$891$	50.6585	1.69712
$892$	14.9300	0.499893
$893$	20.8621	0.698125
$894$	10.7049	0.358026
$895$	−2.24594	−0.0750735
$896$	−1.46435	−0.0489206
$897$	−0.545452	−0.0182121
$898$	24.8314	0.828633
$899$	19.4851	0.649865
$900$	6.50295	0.216765
$901$	20.0655	0.668479
$902$	−50.4213	−1.67885
$903$	4.98189	0.165787
$904$	16.6320	0.553173
$905$	24.2418	0.805825
$906$	51.2472	1.70258
$907$	18.5531	0.616046	0.308023	−	0.951379i	$-0.400333\pi$
$907$	18.5531	0.616046	0.308023	+	0.951379i	$0.400333\pi$
$908$	7.95751	0.264079
$909$	8.07846	0.267946
$910$	1.73186	0.0574107
$911$	−40.3411	−1.33656	−0.668280	−	0.743910i	$-0.732969\pi$
$911$	−40.3411	−1.33656	−0.668280	+	0.743910i	$0.732969\pi$
$912$	−15.4222	−0.510679
$913$	45.8770	1.51831
$914$	−2.67559	−0.0885007
$915$	0.385161	0.0127330
$916$	−18.8118	−0.621558
$917$	0.219568	0.00725078
$918$	−21.6956	−0.716062
$919$	21.6755	0.715008	0.357504	−	0.933912i	$-0.383628\pi$
$919$	21.6755	0.715008	0.357504	+	0.933912i	$0.383628\pi$
$920$	0.945340	0.0311669
$921$	20.3365	0.670111
$922$	−0.824305	−0.0271470
$923$	−5.63986	−0.185638
$924$	−27.9787	−0.920431
$925$	−10.7553	−0.353632
$926$	2.14353	0.0704407
$927$	−3.73280	−0.122601
$928$	2.45914	0.0807253
$929$	−33.5906	−1.10207	−0.551037	−	0.834481i	$-0.685768\pi$
$929$	−33.5906	−1.10207	−0.551037	+	0.834481i	$0.685768\pi$
$930$	58.3352	1.91289
$931$	−25.1355	−0.823781
$932$	25.4066	0.832221
$933$	34.3841	1.12568
$934$	5.09071	0.166573
$935$	40.1288	1.31235
$936$	−2.81218	−0.0919191
$937$	18.9886	0.620331	0.310166	−	0.950683i	$-0.399616\pi$
$937$	18.9886	0.620331	0.310166	+	0.950683i	$0.399616\pi$
$938$	17.6864	0.577482
$939$	−77.8521	−2.54061
$940$	−9.95920	−0.324833
$941$	19.5666	0.637854	0.318927	−	0.947779i	$-0.396678\pi$
$941$	19.5666	0.637854	0.318927	+	0.947779i	$0.396678\pi$
$942$	−52.4733	−1.70967
$943$	3.00764	0.0979422
$944$	12.9777	0.422387
$945$	31.0057	1.00862
$946$	7.32341	0.238105
$947$	−2.11386	−0.0686911	−0.0343456	−	0.999410i	$-0.510935\pi$
$947$	−2.11386	−0.0686911	−0.0343456	+	0.999410i	$0.510935\pi$
$948$	−46.0489	−1.49560
$949$	4.21502	0.136825
$950$	−5.72887	−0.185869
$951$	−98.6831	−3.20002
$952$	3.70788	0.120173
$953$	−52.0120	−1.68483	−0.842416	−	0.538827i	$-0.818868\pi$
$953$	−52.0120	−1.68483	−0.842416	+	0.538827i	$0.818868\pi$
$954$	46.5640	1.50757
$955$	21.3938	0.692287
$956$	−2.25942	−0.0730750
$957$	46.9856	1.51883
$958$	−0.418048	−0.0135065
$959$	29.6238	0.956603
$960$	7.36226	0.237616
$961$	31.7826	1.02524
$962$	4.65110	0.149958
$963$	−1.81072	−0.0583495
$964$	3.98648	0.128396
$965$	63.4456	2.04239
$966$	1.66893	0.0536970
$967$	−17.5625	−0.564771	−0.282385	−	0.959301i	$-0.591126\pi$
$967$	−17.5625	−0.564771	−0.282385	+	0.959301i	$0.591126\pi$
$968$	−30.1288	−0.968378
$969$	39.0504	1.25448
$970$	21.0014	0.674315
$971$	8.77330	0.281549	0.140774	−	0.990042i	$-0.455041\pi$
$971$	8.77330	0.281549	0.140774	+	0.990042i	$0.455041\pi$
$972$	2.17126	0.0696432
$973$	24.7786	0.794366
$974$	−30.1218	−0.965166
$975$	−1.57799	−0.0505360
$976$	0.0523156	0.00167458
$977$	35.0153	1.12024	0.560120	−	0.828412i	$-0.310755\pi$
$977$	35.0153	1.12024	0.560120	+	0.828412i	$0.310755\pi$
$978$	−57.8734	−1.85059
$979$	−115.500	−3.69139
$980$	11.9992	0.383300
$981$	−60.1014	−1.91889
$982$	−41.8209	−1.33456
$983$	24.5933	0.784404	0.392202	−	0.919879i	$-0.371713\pi$
$983$	24.5933	0.784404	0.392202	+	0.919879i	$0.371713\pi$
$984$	23.4234	0.746709
$985$	−44.8329	−1.42849
$986$	−6.22677	−0.198301
$987$	−17.5823	−0.559650
$988$	2.47743	0.0788176
$989$	−0.436843	−0.0138908
$990$	93.1228	2.95964
$991$	−29.6282	−0.941172	−0.470586	−	0.882354i	$-0.655957\pi$
$991$	−29.6282	−0.941172	−0.470586	+	0.882354i	$0.655957\pi$
$992$	7.92354	0.251573
$993$	2.90574	0.0922109
$994$	17.2564	0.547340
$995$	60.5425	1.91933
$996$	−21.3123	−0.675305
$997$	−14.0223	−0.444092	−0.222046	−	0.975036i	$-0.571273\pi$
$997$	−14.0223	−0.444092	−0.222046	+	0.975036i	$0.571273\pi$
$998$	16.5086	0.522570
$999$	83.2692	2.63452

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6002.2.a.b.1.6	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6002.2.a.b.1.6	✓	56	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6002 = 2 \cdot 3001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6002.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.97926 q^{3} +1.00000 q^{4} -2.47117 q^{5} +2.97926 q^{6} +1.46435 q^{7} -1.00000 q^{8} +5.87597 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.97926 q^{3} +1.00000 q^{4} -2.47117 q^{5} +2.97926 q^{6} +1.46435 q^{7} -1.00000 q^{8} +5.87597 q^{9} +2.47117 q^{10} +6.41318 q^{11} -2.97926 q^{12} +0.478590 q^{13} -1.46435 q^{14} +7.36226 q^{15} +1.00000 q^{16} -2.53209 q^{17} -5.87597 q^{18} +5.17652 q^{19} -2.47117 q^{20} -4.36269 q^{21} -6.41318 q^{22} +0.382547 q^{23} +2.97926 q^{24} +1.10670 q^{25} -0.478590 q^{26} -8.56826 q^{27} +1.46435 q^{28} -2.45914 q^{29} -7.36226 q^{30} -7.92354 q^{31} -1.00000 q^{32} -19.1065 q^{33} +2.53209 q^{34} -3.61867 q^{35} +5.87597 q^{36} -9.71833 q^{37} -5.17652 q^{38} -1.42584 q^{39} +2.47117 q^{40} +7.86215 q^{41} +4.36269 q^{42} -1.14193 q^{43} +6.41318 q^{44} -14.5205 q^{45} -0.382547 q^{46} +4.03015 q^{47} -2.97926 q^{48} -4.85567 q^{49} -1.10670 q^{50} +7.54375 q^{51} +0.478590 q^{52} -7.92448 q^{53} +8.56826 q^{54} -15.8481 q^{55} -1.46435 q^{56} -15.4222 q^{57} +2.45914 q^{58} +12.9777 q^{59} +7.36226 q^{60} +0.0523156 q^{61} +7.92354 q^{62} +8.60450 q^{63} +1.00000 q^{64} -1.18268 q^{65} +19.1065 q^{66} -12.0780 q^{67} -2.53209 q^{68} -1.13971 q^{69} +3.61867 q^{70} -11.7843 q^{71} -5.87597 q^{72} +8.80716 q^{73} +9.71833 q^{74} -3.29715 q^{75} +5.17652 q^{76} +9.39116 q^{77} +1.42584 q^{78} +15.4565 q^{79} -2.47117 q^{80} +7.89912 q^{81} -7.86215 q^{82} +7.15355 q^{83} -4.36269 q^{84} +6.25724 q^{85} +1.14193 q^{86} +7.32642 q^{87} -6.41318 q^{88} -18.0098 q^{89} +14.5205 q^{90} +0.700826 q^{91} +0.382547 q^{92} +23.6063 q^{93} -4.03015 q^{94} -12.7921 q^{95} +2.97926 q^{96} +8.49856 q^{97} +4.85567 q^{98} +37.6836 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9}+O(q^{10}) \) 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9	\( 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9} + 12 q^{11} - 11 q^{12} - 31 q^{13} + 21 q^{14} - 22 q^{15} + 56 q^{16} - 4 q^{17} - 53 q^{18} - 9 q^{19} + 13 q^{21} - 12 q^{22} - 39 q^{23} + 11 q^{24} + 8 q^{25} + 31 q^{26} - 44 q^{27} - 21 q^{28} + 13 q^{29} + 22 q^{30} - 35 q^{31} - 56 q^{32} - 26 q^{33} + 4 q^{34} - 7 q^{35} + 53 q^{36} - 65 q^{37} + 9 q^{38} - 27 q^{39} + 38 q^{41} - 13 q^{42} - 76 q^{43} + 12 q^{44} - 21 q^{45} + 39 q^{46} - 43 q^{47} - 11 q^{48} + 9 q^{49} - 8 q^{50} - 19 q^{51} - 31 q^{52} - 26 q^{53} + 44 q^{54} - 67 q^{55} + 21 q^{56} - 26 q^{57} - 13 q^{58} + 11 q^{59} - 22 q^{60} - 17 q^{61} + 35 q^{62} - 67 q^{63} + 56 q^{64} + 31 q^{65} + 26 q^{66} - 93 q^{67} - 4 q^{68} - 13 q^{69} + 7 q^{70} - 33 q^{71} - 53 q^{72} - 41 q^{73} + 65 q^{74} - 21 q^{75} - 9 q^{76} + 5 q^{77} + 27 q^{78} - 69 q^{79} + 36 q^{81} - 38 q^{82} + 4 q^{83} + 13 q^{84} - 40 q^{85} + 76 q^{86} - 69 q^{87} - 12 q^{88} + 40 q^{89} + 21 q^{90} - 64 q^{91} - 39 q^{92} - 57 q^{93} + 43 q^{94} - 22 q^{95} + 11 q^{96} - 71 q^{97} - 9 q^{98} + 17 q^{99}+O(q^{100}) \) 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9 + 12 * q^11 - 11 * q^12 - 31 * q^13 + 21 * q^14 - 22 * q^15 + 56 * q^16 - 4 * q^17 - 53 * q^18 - 9 * q^19 + 13 * q^21 - 12 * q^22 - 39 * q^23 + 11 * q^24 + 8 * q^25 + 31 * q^26 - 44 * q^27 - 21 * q^28 + 13 * q^29 + 22 * q^30 - 35 * q^31 - 56 * q^32 - 26 * q^33 + 4 * q^34 - 7 * q^35 + 53 * q^36 - 65 * q^37 + 9 * q^38 - 27 * q^39 + 38 * q^41 - 13 * q^42 - 76 * q^43 + 12 * q^44 - 21 * q^45 + 39 * q^46 - 43 * q^47 - 11 * q^48 + 9 * q^49 - 8 * q^50 - 19 * q^51 - 31 * q^52 - 26 * q^53 + 44 * q^54 - 67 * q^55 + 21 * q^56 - 26 * q^57 - 13 * q^58 + 11 * q^59 - 22 * q^60 - 17 * q^61 + 35 * q^62 - 67 * q^63 + 56 * q^64 + 31 * q^65 + 26 * q^66 - 93 * q^67 - 4 * q^68 - 13 * q^69 + 7 * q^70 - 33 * q^71 - 53 * q^72 - 41 * q^73 + 65 * q^74 - 21 * q^75 - 9 * q^76 + 5 * q^77 + 27 * q^78 - 69 * q^79 + 36 * q^81 - 38 * q^82 + 4 * q^83 + 13 * q^84 - 40 * q^85 + 76 * q^86 - 69 * q^87 - 12 * q^88 + 40 * q^89 + 21 * q^90 - 64 * q^91 - 39 * q^92 - 57 * q^93 + 43 * q^94 - 22 * q^95 + 11 * q^96 - 71 * q^97 - 9 * q^98 + 17 * q^99

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